WASHINGTON — A coalition of prominent Democrats, including many from New England, slammed President Obama’s $3.8 trillion budget blueprint Wednesday for its proposed changes to the Social Security payment formula and Medicare, opening a widening rift between the president and members of his own party.

Senator Elizabeth Warren of Massachusetts said she was shocked by Obama’s proposal to recalculate the cost of living adjustment for Social Security beneficiaries by linking it to a different version of the Consumer Price Index, known as the “chained CPI.”

The switch would mean the growth of benefits would slow and no longer keep pace with the current measure of price increases on such necessities such as food and health care.

Advertisement - Continue Reading Below

“In short, ‘chained CPI’ is just a fancy way to say ‘cut benefits for seniors, the permanently disabled, and orphans,’” Warren fired off in an e-mail to supporters. She related the experience of her brother, David Herring, a military veteran and former small business owner who lives on monthly Social Security checks of $1,100. “Our Social Security system is critical to protecting middle-class families,’’ she wrote, “and we cannot allow it to be dismantled inch by inch.”

Obama’s proposal to rein back on so-called entitlement programs in exchange for raising taxes on corporations and the biggest earners is unpopular with large segments of both parties. GOP leaders, while calling for tempering the cost of social programs, have indicated they would not support further tax increases to get them.

But it was the uncharacteristic criticism from his own party Wednesday that was often loudest.

Representative Edward Markey of Massachusetts called “chained CPI” an abbreviation for “Cutting People’s Income, a wrong-headed change that would go back on the promise we make to our senior citizens.”

“Tea Party Republicans may have pushed the president into many of these difficult decisions, but it still does not make this budget right nor fair, especially for those Americans who need help the most,” Markey said.

Representative Stephen Lynch, who is running against Markey for Senate, said that if elected, he promises to filibuster in the Senate to prevent any cuts to Social Security.

“I respect and admire President Obama, but I feel that the negotiations over taxes with the Republicans have forced him into a bad deal and he is going down the wrong road on chained CPI,” Lynch said. “I would gladly take to the Senate floor in defense of our seniors.”

Some observers expressed surprise at the extent of the rift between Democrats and the White House over the Social Security and Medicare proposals.

“I have never really seen anything like this,” said Jim Manley, a former top aide to Senate majority leader Harry Reid and now a Democratic strategist. “The opposition is pretty widespread and somewhat fierce.”

In making good on his promise to slash the deficit, caused partly by rising entitlement costs, Obama has taken a risk he has acknowledged in his quest to exact a compromise on taxes from Republicans.

At his Rose Garden press conference Wednesday, Obama said that the proposed changes in Social Security and Medicare — which he had offered privately to House Speaker John Boehner in December in failed budget talks — are not “optimal” but that “I’m willing to accept them as part of a compromise — if, and only if, they contain protections for the most vulnerable Americans.”

“The rising cost of caring for an aging generation is the single biggest driver of our long-term deficits,” Obama said. He has also proposed further reductions to some Medicare providers, a move that has upset hospital executives.

The Medicare cuts include reducing special payments to teaching hospitals that help them maintain the newest and most advanced services and equipment to train physicians, such as 24-hour trauma and burn units. In addition, wealthier seniors would be asked to contribute more, and beneficiaries would pay a surcharge for supplemental coverage that helps with copays associated with doctor visits, said the National Committee to Preserve Social Security & Medicare.

Obama, who planned to have dinner with select Senate Republicans Wednesday evening, emphasized that any changes in entitlement programs must go hand-in-hand with reforming the tax code to make the nation’s wealthiest individuals and corporations pay more.

“These measures will only become law if congressional Republicans agree to meet me in the middle by eliminating special tax breaks and loopholes so millionaires and billionaires do their fair share to cut the deficit,” Obama wrote in his budget message. “I am willing to make tough choices that may not be popular within my own party, because there can be no sacred cows for either party.”

Dozens of Democrats in Congress have already responded with a resounding “no.” Representatives Alan Grayson of Florida and Mark Takano of California co-wrote a letter to Obama that outlines their intention to vote against “any and every cut to Medicare, Medicaid, and Social Security benefits — including raising the retirement age or cutting the cost of living adjustments that our constituents earned and need.”

The letter has been signed by at least 30 House members, including Lynch, Markey, James McGovern, also of Massachusetts.

Two other New England senators who usually back the president had harsh words for his Social Security proposal.

“I made a promise to the people of Rhode Island that I would always oppose cuts to Social Security, and I’m going to keep that promise,” said Senator Sheldon Whitehouse. “Social Security is fully solvent for the next 20 years, has not contributed to our budget deficits, and has no place in this debate over federal spending.”

Vermont independent Bernie Sanders, who sponsored an amendment to a recent Senate budget measure to reject the chained CPI plan, said last week that he would “do everything in my power to block President Obama’s proposal’’ to change the benefits formula for Social Security recipients.

As chairman of the Senate Committee on Veterans Affairs, Sanders said he is especially concerned about the impact the change would have on disabled veterans and their survivors.

The ranks of New England Democrats lining up to oppose the president’s approach have grown steadily in recent weeks.

“I have serious concerns with the proposed cuts to Medicare and Social Security benefits and do not believe these are the reforms that best serve our seniors or our economy,” Representative John Tierney of Massachusetts, said Wednesday.

Representative Chellie Pingree, a Maine Democrat, said she, too, would vote against the Obama Social Security plan.

“For someone who retires today, that cut would mean they would be getting $650 less a year when they are 75 and over $1,100 less a year when they reach age 85,” Pingree said.

Aside from the Social Security proposal, Markey praised Obama’s proposal to increase research funding, infusing the National Institutes of Health with a $400 million increase from fiscal year 2012 levels.

The White House budget also replaces research cuts resulting from the across-the-board cuts known as sequestration, adding $128 million in NIH funding back to Massachusetts starting in FY 2014, which begins in October, according to a Markey staffer who analyzed the White House budget’s impact on Massachusetts.

The Bay State generally gets 10 percent of all NIH grants, and Obama’s research budget would benefit the Massachusetts economy and save jobs, said the Markey staffer.